1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
saul85 [17]
3 years ago
10

(a) A shipment of 120 fasteners that contains 4 defective fasteners was sent to a manufacturing plant. The quality-control manag

er at the manufacturing plant randomly selects 5 fasters and inspects them. What is the probability that exactly 1 fastener is defective? (b) The Energy Information Administration (EIA) sampled 900 retail gasoline outlets and reported that, the national average gasoline price for regular-grade gasoline to be $4.113 per gallon with a standard deviation of $0.11 per gallon. Construct a 95% Confidence Interval for mean price of regular-grade gasoline price.
Mathematics
1 answer:
denis-greek [22]3 years ago
7 0

Answer:

a)  Probability that exactly 1 fastener is defective, P(X = 1) = 0.144

b) Confidence interval for mean price, CI = [4.1058, 4.1202]

Step-by-step explanation:

a) Total number of fasteners = 120

Number of defective fasteners = 4

Probability of selecting a defective fastener, p = 4/120

p = 0.033

Probability of selecting an undefective fastener, q = 1 - p

q = 1 - 0.033

q = 0.967

5 fasteners were randomly selected, n =5

Probability that exactly one fastener is defective:

P(X =r) = (nCr) p^r q^{n-r}\\P(X =1) = (5C1) 0.033^1 0.967^{5-1}\\P(X =1) = 0.144

b) Number of gasoline outlets sampled, n = 900

Average gasoline price, \bar{x} = 4.113

Standard deviation, \sigma = 0.11

Confidence Level, CL = 95% = 0.95

Significance level, \alpha = 1 - 0.95 = 0.05

\alpha/2 = 0.05/2 = 0.025

From the standard normal table, z_{\alpha/2} = z_{0.025} = 1.96

error margin can be calculated as follows:

e_{margin} = z_{\alpha/2} * \frac{\sigma}{\sqrt{n} } \\e_{margin} = 1.96 * \frac{0.11}{\sqrt{900} }\\e_{margin} = 0.0072

The confidence interval will be given as:

CI = \bar{x} \pm e_{margin}  \\CI = 4.113 \pm 0.0072\\CI = [(4.113-0.0072), (4.113+0.0072)]\\CI = [4.1058, 4.1202]

You might be interested in
Bill spent 2/3 of an hour swimming and 5/6 of an hour jogging. How much longer did he jog than swim
Zinaida [17]
Bill jogged 1/6 longer than he swam.
Hope this helps!!

6 0
2 years ago
Read 2 more answers
Train A & train B leave a central station at the same time. They travel at the same speed, but one in opposite directions, w
saul85 [17]

you can do it, man
I believe in you
7 0
3 years ago
Need help ASAP answer ASAP
Feliz [49]

Answer:

1A= 27+43= 70

Step-by-step explanation:

you add the values of each thing they are asking so for the next one you would do, Cakes Plus Biscuits. So 86+59 and that will give you your answer for 1B

6 0
2 years ago
How do u spell 5,165,874 in word form
Novay_Z [31]
Five million one hundred sixty five thousand eight hundred seventy four.
4 0
3 years ago
Read 2 more answers
HELP I NEED HELP ASAP
eimsori [14]

Answer:

I think its D

Step-by-step explanation:

You can rule out A and B because he would be able to throw it farther than 30 ft do that leaves C and D but davis Couldn't throw a 9.1 lb ball 30 ft so the answer is D

3 0
2 years ago
Other questions:
  • I WILL RATE YOU BRAINLIEST. I REALLY NEED HELP!!! I already tried 12.8 but that didn't work
    9·2 answers
  • Please answer problems 7 and 8 ASAP!
    11·2 answers
  • What’s 29/50 as decimal
    13·1 answer
  • What is the best approximation for the area of a circle with a diameter of 13 meters?
    7·1 answer
  • Compare 3 x 10^4 and 6 x 10^3
    7·1 answer
  • What would be the original cost? $99.50?
    9·1 answer
  • Which of the following represents a function?
    9·2 answers
  • Find the equation that has a slope of 4 and passes through the point (1,-2)​
    11·1 answer
  • frank went went on a road trip. After 3 hours, he noticed that he drove 195 miles. if he countinues to travel rate, how many mil
    8·1 answer
  • &gt;<br> How many 3 card hands are possible with a 48-card deck?<br> The number of 3 card hands is a
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!